Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D
1
has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s
$-1
. Disc D
2
has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s
-1
. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s
-$1
) of the system is